I believe sky cut refers to making a subset of the data of the full sky field - most frequently when looking at the CMB data from WMAP.

Since our own galaxy makes a lot of K band (23 ghz) noise it tends to swamp out the detection of the CMB in that part of the sky occupied by the Milky Way. To look at cleaner data not affected by this area of the sky a mask may be employed to drop out these dominating data sets - a sky cut - as in cutting out part of the data - that interferes with viewing the CMB.

Perhaps others have better explanations and can elaborate or extend my understanding of it, but that at least is what I think it means when I read the literature.